drawing square root of an unknown function with a double root.

Question

Without the equation of the function $y=f(x)$ and only the diagram, how would you draw $y=\sqrt{f(x)}$ and why?

I am most interested in root if it looks like a double root but not necessarily a parabola?

ie. 1. concave up

2. absolute value

3. cusp

Thanks! please see link for images

http://we.tl/onxXcPXxAF

Answer 1

If the graph is more rounded than a parabola at a point where it touches the $x$-axis, then its square-root would be rounded there too, having zero gradient. If it is less rounded, then its square-root would have a cusp there with infinite gradient on both sides. If it is equally rounded, then its square-root would have a straight corner there.

The problem is that you may need to zoom in very far to determine which of the three cases it is.

Answer 2

Thanks!

After more investigation, I made this.

http://tube.geogebra.org/m/1500615